THE ACTUAL PROBLEMS OF THE MODERN TRANSLATION OF MATHEMATICAL TEXTS

The article investigates a high-quality modern translation of mathematical texts, which requires intensive research in the subject of the source text. The question of the names of new geometries, some geometric terms and their translation, taking into account the historical aspect of their occurrence, which cover the peculiarities of the English established mathematical names, is considered. It is shown that during the translation process it is necessary to focus on the general content of the sentence, understanding its meaning and to know the historical genesis of the development of mathematical science. In this context, some historical facts relating to the names of new geometries, including the geometry of Lobachevsky, Riman, Euler, are given. The history of the study of constructions in the non-Euclidean geometry of Lobachevsky is studied, which became one of the directions of the development of its ideas by the Ukrainian school of mathematicians-geometers. This requires the coherence of translations of Ukrainian and English with a summary to a high standard of use of terms. It is proved that the names of geometries adopted in Eastern Europe have their own Slavic aspect (Lobachevsky's geometry) that in Western Europe they are not used names, and names are found with mathematical features (hyperbolic geometry, elliptic geometry, parabolic geometry) .